Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
from bisect import bisect_left 

def BinarySearch(a, x): 
    i = bisect_left(a, x) 
    if i != len(a) and a[i] == x: 
        return i 
    else: 
        return -1
num = int(input())


nums = []
for n in range(1,num):
    nt = n*(n+1)//2
    if nt<num:
        nums.append(nt)
    elif nt>=num:
        break
    


passe = False
for n in nums:
    if BinarySearch(nums,num-n)!=-1:
        passe =True
        
    
if passe : print("YES")
else: print("NO")